Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force

The spherical polar components of the Coriolis force consist of terms in sin ϕ and terms in cos ϕ, where ϕ is latitude (referred to the frame-rotation vector as polar axis). The cos ϕ Coriolis terms are not retained in the usual hydrostatic primitive equations of numerical weather prediction and climate simulation, their neglect being consistent with the shallow-atmosphere approximation and the simultaneous exclusion of various small metric terms. Scale analysis for diabatically driven, synoptic-scale motion in the tropics, and for planetary-scale motion, suggests that the cos ϕ Coriolis terms may attain magnitudes of order 10% of those of key terms in the hydrostatic primitive equations. It is argued that the cos ϕ Coriolis terms should be included in global simulation models. A global, quasi-hydrostatic model having a complete representation of the Coriolis force is proposed. Conservation of axial angular momentum and potential vorticity, as well as energy, is achieved by a formulation in which all metric terms are retained and the shallow-atmosphere approximation is relaxed. Distance from the centre of the earth is replaced by a pseudo-radius which is a function of pressure only. This model is put forward as a more accurate alternative to the traditional hydrostatic primitive equations; it preserves the desired conservation laws and may be integrated by broadly similar grid-point methods.